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Simplifying x2 + -37x + -84 = 0 Reorder the terms: -84 + -37x + x2 = 0 Solving -84 + -37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -37x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -37x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -37x + x2 = 0 + 84 -37x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -37x + x2 = 84 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = 84 + 342.25 Reorder the terms: 342.25 + -37x + x2 = 84 + 342.25 Combine like terms: 84 + 342.25 = 426.25 342.25 + -37x + x2 = 426.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 426.25 Calculate the square root of the right side: 20.645822822 Break this problem into two subproblems by setting (x + -18.5) equal to 20.645822822 and -20.645822822.Subproblem 1
x + -18.5 = 20.645822822 Simplifying x + -18.5 = 20.645822822 Reorder the terms: -18.5 + x = 20.645822822 Solving -18.5 + x = 20.645822822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 20.645822822 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 20.645822822 + 18.5 x = 20.645822822 + 18.5 Combine like terms: 20.645822822 + 18.5 = 39.145822822 x = 39.145822822 Simplifying x = 39.145822822Subproblem 2
x + -18.5 = -20.645822822 Simplifying x + -18.5 = -20.645822822 Reorder the terms: -18.5 + x = -20.645822822 Solving -18.5 + x = -20.645822822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -20.645822822 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -20.645822822 + 18.5 x = -20.645822822 + 18.5 Combine like terms: -20.645822822 + 18.5 = -2.145822822 x = -2.145822822 Simplifying x = -2.145822822Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.145822822, -2.145822822}
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